A new sixth-order approximation for nonlinear two-point boundary value problems: application of single-step alternating group explicit iteration method to engineering problems

Engineering with Computers - Tập 37 - Trang 3541-3550 - 2020
Pinaki Ranjan Mohanty1
1Department of Computer Science, College of Science, Purdue University, West Lafayette, USA

Tóm tắt

We report a new three-point compact sixth-order approximation for the solution of nonlinear two-point boundary value problems $$ {-}w^{\prime\prime} + f\left( {t,w} \right) = 0 $$ , subject to natural boundary conditions prescribed at two end points. We also discuss the application of single-step alternating group explicit (SAGE) iteration method to the nonlinear difference equation as a computational tool. The error analysis of the SAGE iteration method is discussed briefly. We have compared the results obtained by using the proposed SAGE iteration method with the results obtained by corresponding two-step alternating group explicit iteration method to demonstrate experimentally the superiority of the proposed method.

Tài liệu tham khảo

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